Load libraries

library(tidyverse) # data manipulation
library(ggpubr) # producing data exploratory plots
library(modelsummary) # descriptive data 
library(glmmTMB) # running generalised mixed models 
library(DHARMa) # model diagnostics 
library(performance) # model diagnostics  
library(ggeffects) # partial effect plots 
library(car) # running Anova on model 
library(emmeans) # post-hoc analysis

Import data

df_adults <- read_csv("resp_results_adults.csv")
df_jresp <- read_csv("resp_results_juveniles.csv")

Data manipulation

Adults

df_adults_cleaned <- df_adults |> 
  mutate(FISH_ID = factor(FISH_ID), 
         Sex = factor(Sex), 
         Population = factor(Population), 
         Tank = factor(Tank), 
         Chamber = factor(Chamber), 
         System =factor(System), 
         Temperature =factor(Temperature), 
         True_resting=factor(True_resting)) 

df_males <- df_adults_cleaned |> 
  filter(Sex == "M")
df_females <- df_adults_cleaned |> 
  filter(Sex == "F")

df_adults_cleaned2 <- df_males |> 
  full_join(select(df_females, c("Tank","Temperature","Mass","Resting","Max","AAS","FISH_ID","Sex")), by="Tank") |> 
  mutate(Temperature.x = coalesce(Temperature.x, Temperature.y), 
         FISH_ID.x = coalesce(FISH_ID.x, FISH_ID.y),
         Sex.x = coalesce(Sex.x, Sex.y),
         Resting.midpoint = (Resting.x+Resting.y)/2, 
         Max.midpoint = (Max.x+Max.y)/2, 
         AAS.midpoint = (AAS.x+AAS.y)/2)

Juveniles

df_jresp$Population <-  fct_collapse(df_jresp$Population, 
                                      `Vlassof cay`= c("Vlassof reef", "Vlassof", "Vlassof Cay", "Vlassof cay"), 
                                      `Arlington reef` = c("Arlington reef","Arlginton reef")) 

#df_jresp$Female <-  fct_collapse(df_jresp$Female, 
                                  #`CARL359`= c("CARL359", "CARL59")) 


df_jresp2 <-  df_jresp |> 
  unite("F0", c("Male","Female"), sep="_", remove=FALSE) |>
  mutate(across(1:7, factor), 
         Temperature = factor(Temperature), 
         True_resting = factor(True_resting)) 

#df_jresp2_rest <- df_jresp2 |> 
  #filter(True_resting == "Y")

Merging dataframes

temp1a <- df_jresp2 |> 
  mutate(FISH_ID.x = Male)
temp1b <- df_jresp2 |> 
  mutate(FISH_ID.y = Female)
temp2a <- temp1a |> 
  left_join(select(df_adults_cleaned2, c("FISH_ID.x",
                                          "Sex.x",
                                          "Resting.x", 
                                          "Max.x", 
                                          "AAS.x", 
                                          "Mass.x")), 
                    by="FISH_ID.x")
temp2b <- temp1b |> 
  left_join(select(df_adults_cleaned2, c("FISH_ID.y",
                            "Sex.y",
                            "Resting.y", 
                            "Max.y", 
                            "AAS.y", 
                            "Mass.y")), 
                   by="FISH_ID.y") 
df_merged <- temp2a |> 
  left_join(select(temp2b, c("Clutch","Replicate", 
                             "FISH_ID.y",
                             "Resting.y", 
                             "Max.y", 
                             "AAS.y", 
                             "Mass.y")), 
            by=c("Clutch","Replicate"))
df <- df_merged |> 
  mutate(Resting_MALE =Resting.x, 
         Max_MALE =Max.x, 
         AAS_MALE =AAS.x, 
         Mass_MALE =Mass.x, 
         FISH_ID.y =FISH_ID.x,#makes more sense for males to be .y instead of .x
         FISH_ID.x =FISH_ID.x, 
         Resting_FEMALE =Resting.y, 
         Max_FEMALE =Max.y, 
         AAS_FEMALE =AAS.y, 
         Mass_FEMALE =Mass.y) |> 
  mutate(Resting_MID =(Resting_MALE+Resting_FEMALE)/2, 
         Max_MID =(Max_MALE+Max_FEMALE)/2, 
         AAS_MID =(AAS_MALE+AAS_FEMALE)/2) |> # easier to do it again
  filter(True_resting == "Y") # this should remove 10 individuals from the df

Exploratory analysis

Offspring-Male

plot1 <- ggplot(df, aes(x=Resting_MALE, y=Resting, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-male relationship") + 
  xlab("") + 
  ylab("Resting (parental-male)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot2 <- ggplot(df, aes(x=Max_MALE, y=Max, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-male relationship") +
  xlab("") + 
  ylab("Max (parental-male)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot3 <- ggplot(df, aes(x=AAS_MALE, y=AAS, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-male relationship") +
  xlab("") + 
  ylab("AAS (parental-male)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot4 <- ggplot(df, aes(x=Resting_MALE, y=Resting, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-male relationship") + 
  xlab("Resting (offspring)") + 
  ylab("Resting (parental-male)") +
  theme_classic() + 
  theme(legend.position = "bottom")

plot5 <- ggplot(df, aes(x=Max_MALE, y=Max, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-male relationship") +
  xlab("Max (offspring)") + 
  ylab("Max (parental-male)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot6 <- ggplot(df, aes(x=AAS_MALE, y=AAS, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-male relationship") +
  xlab("AAS (offspring)") + 
  ylab("AAS (parental-male)") +
  theme_classic() + 
  theme(legend.position = 'none') 

ggarrange(plot1, plot2, plot3, 
          plot4, plot5, plot6,
          ncol = 3, 
          nrow = 3)

Offspring-Female

plot1 <- ggplot(df, aes(x=Resting_FEMALE, y=Resting, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-female relationship") + 
  xlab("") + 
  ylab("Resting (parental-female)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot2 <- ggplot(df, aes(x=Max_FEMALE, y=Max, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-female relationship") +
  xlab("") + 
  ylab("Max (parental-female)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot3 <- ggplot(df, aes(x=AAS_FEMALE, y=AAS, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-female relationship") +
  xlab("") + 
  ylab("AAS (parental-female)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot4 <- ggplot(df, aes(x=Resting_FEMALE, y=Resting, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-female relationship") + 
  xlab("Resting (offspring)") + 
  ylab("Resting (parental-female)") +
  theme_classic() + 
  theme(legend.position = "bottom")

plot5 <- ggplot(df, aes(x=Max_FEMALE, y=Max, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-female relationship") +
  xlab("Max (offspring)") + 
  ylab("Max (parental-female)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot6 <- ggplot(df, aes(x=AAS_FEMALE, y=AAS, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-female relationship") +
  xlab("AAS (offspring)") + 
  ylab("AAS (parental-female)") +
  theme_classic() + 
  theme(legend.position = 'none') 

ggarrange(plot1, plot2, plot3, 
          plot4, plot5, plot6,
          ncol = 3, 
          nrow = 3)

Offspring-Midpoint

plot1 <- ggplot(df, aes(x=Resting_MID, y=Resting, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-midpoint relationship") + 
  xlab("") + 
  ylab("Resting (parental-midpoint)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot2 <- ggplot(df, aes(x=Max_MID, y=Max, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-midpoint relationship") +
  xlab("") + 
  ylab("Max (parental-midpoint)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot3 <- ggplot(df, aes(x=AAS_MID, y=AAS, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-midpoint relationship") +
  xlab("") + 
  ylab("AAS (parental-midpoint)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot4 <- ggplot(df, aes(x=Resting_MID, y=Resting, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-midpoint relationship") + 
  xlab("Resting (offspring)") + ylab("Resting (parental-midpoint)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot5 <- ggplot(df, aes(x=Max_MID, y=Max, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-midpoint relationship") +
  xlab("Max (offspring)") + ylab("Max (parental-midpoint)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot6 <- ggplot(df, aes(x=AAS_MID, y=AAS, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-midpoint relationship") +
  xlab("AAS (offspring)") + ylab("AAS (parental-midpoint)") +
  theme_classic() + 
  theme(legend.position = 'none') 

ggarrange(plot1, plot2, plot3, 
          plot4, plot5, plot6,
          ncol = 3, 
          nrow = 3, 
          common.legend = TRUE)

Descriptive statistics

Juveniles - overview

Overview

tinytable_80gv3idas3qvz4292kct
Population 27 28.5 30
Arlington reef 58 42 52
Pretty patches 25 21 34
Sudbury reef 26 15 16
Vlassof cay 25 10 25 
datasummary(Factor(F0) ~ Factor(Temperature), 
            data = df, 
            fmt = "%.0f")
tinytable_ctgpu770l4u4iqqcwcuq
F0 27 28.5 30
CARL217_CARL226 0 8 0
CARL218_CARL222 0 0 13
CARL230_CARL235 12 0 0
CARL233_CARL215 0 0 8
CARL237_CARL219 10 0 0
CARL241_CARL239 15 0 0
CARL249_CARL360 0 0 8
CARL335_CARL359 0 13 0
CARL338_CARL345 0 8 0
CARL344_CARL370 0 0 15
CARL354_CARL355 21 0 0
CARL360_CARL249 0 0 8
CARL367_CARL363 0 7 0
CARL369_CARL349 0 6 0
CPRE189_CPRE202 0 0 15
CPRE372_CPRE209 6 0 0
CPRE372_CPRE370 8 0 0
CPRE375_CPRE377 11 0 0
CPRE391_CPRE390 0 0 6
CPRE447_CPRE452 0 0 13
CPRE453_CPRE459 0 7 0
CPRE521_CPRE524 0 7 0
CPRE550_CPRE533 0 7 0
CSUD002_CSUD213 0 8 0
CSUD009_CSUD212 13 0 0
CSUD013_CSUD017 13 0 0
CSUD016_CSUD078 0 7 0
CSUD312_CSUD304 0 0 16
CVLA049_CVLA098 0 10 0
CVLA089_CVLA059 0 0 7
CVLA102_CVLA466 6 0 0
CVLA106_CVLA091 0 0 12
CVLA468_CVLA477 12 0 0
CVLA486_CVLA463 7 0 0
CVLA498_CVLA493 0 0 6

Juveniles

Resting oxygen uptake

tinytable_sp1t40oq6tpozfbk63wo
Temperature NUnique mean median min max sd Histogram
27 132 0.21 0.21 0.08 0.64 0.08 ▃▆▇▆▁▁
28.5 88 0.24 0.23 0.09 0.47 0.08 ▂▄▆▆▇▄▁▁ ▁
30 127 0.23 0.23 0.06 0.40 0.07 ▁▂▃▅▇▅▅▄▁▁

Maximum oxygen uptake

tinytable_3wy5tmz71k7u1g2zd9h5
Temperature NUnique mean median min max sd Histogram
27 127 0.58 0.55 0.27 1.66 0.19 ▄▇▆▃▂
28.5 84 0.66 0.64 0.24 1.08 0.18 ▂▅▇▇▇▃▄▂▂
30 126 0.65 0.64 0.16 1.29 0.19 ▂▃▇▅▆▃▁

Absolute aerobic scope

tinytable_am2xuuo3y47pmwtprgqh
Temperature NUnique mean median min max sd Histogram
27 125 0.37 0.34 0.14 1.02 0.14 ▃▇▇▄▃▂
28.5 84 0.42 0.40 0.10 0.79 0.15 ▁▃▅▇▅▃▅▃▁▁
30 126 0.42 0.41 0.09 0.99 0.15 ▁▄▆▄▇▃▁

Adults - overview

Overview

datasummary(Factor(Population) ~ Factor(Temperature), 
            data = df_adults_cleaned, 
            fmt = "%.0f")
tinytable_ojc3p6geokkeslezqs3q
Population 27 28.5 30
Arlington reef 8 7 4
Pretty patches 4 6 4
Sudbury reef 4 3 2
Vlassof cay 6 2 5 
datasummary(Factor(Population) ~ Factor(Temperature)*Factor(Sex), 
            data = df_adults_cleaned, 
            fmt = "%.0f")
tinytable_vrtdafv4fqwlps8lj5ae
27 28.5 30
Population F M F M F M
Arlington reef 4 4 2 5 2 2
Pretty patches 2 2 3 3 3 1
Sudbury reef 2 2 1 2 1 1
Vlassof cay 3 3 1 1 3 2

Pairs

datasummary(Factor(Population)*Factor(Temperature.x) ~ AAS.midpoint*(NUnique), 
            data = df_adults_cleaned2, 
            fmt = "%.0f")
tinytable_r3i19iz91ikayq3tcz0j
Population Temperature.x NUnique
Arlington reef 27 3
28.5 2
30 2
Pretty patches 27 2
28.5 3
30 1
Sudbury reef 27 2
28.5 2
30 1
Vlassof cay 27 3
28.5 1
30 2

Adults

Resting oxygen uptake

tinytable_7vdvqq4u1k0g9jd65hsd
Temperature NUnique mean median min max sd Histogram
27 22 6.29 6.06 3.82 10.09 1.56 ▂▂▃▇▂▂▁▁▁▁
28.5 18 6.49 6.96 4.35 8.49 1.45 ▇▂▅▂▃▃▅▃
30 15 7.29 7.20 5.14 9.15 1.46 ▅▂▇▂▂▂▇▇

Maximum oxygen uptake

tinytable_hfk87vt0b4dl3t2doe5f
Temperature NUnique mean median min max sd Histogram
27 22 16.58 16.91 9.70 22.06 3.36 ▃▃▅▅▃▃▅▇▂
28.5 18 17.09 17.23 11.04 28.39 3.94 ▅▂▅▇▇▃▂
30 15 16.48 16.83 11.78 21.24 2.82 ▂▃▂▃▇▂▂▃▂

Absolute aerobic scope

tinytable_hqym8n1fwcu7ux2mvivc
Temperature NUnique mean median min max sd Histogram
27 22 10.29 10.26 3.85 16.28 3.14 ▃▁▄▇▃▆▃▃▁
28.5 18 10.59 9.66 6.11 20.44 3.66 ▅▅▇▇▃▂▂
30 15 9.19 9.16 4.36 12.77 2.91 ▃▂▅▂▂▂▃▇

Fit Models [random factors]

model1 <- glmmTMB(Resting ~ (1|Clutch), 
                  family="gaussian",
                  data = df) 

model2 <- glmmTMB(Resting ~ (1|Clutch) + (1|Population), 
                  family="gaussian",
                  data = df) 

model3 <- glmmTMB(Resting ~ (1|Clutch) + (1|Chamber), 
                  family="gaussian",
                  data = df) 

model4 <- glmmTMB(Resting ~ (1|Clutch) + (1|Population) + (1|Chamber), 
                  family="gaussian",
                  data = df)
Model selection
AIC(model1, model2, model3, model4, k=2)
BIC(model1, model2, model3, model4)

Model1 performs the best therefore only Clutch will be used as a random factor in future models

Relationships

Offspring-Male

Fit model [fixed factors]

After figuring out which random factors will be incorporated into the model we will start to examine out fixed factors. Some fixed factors such as Resting_(FE)MALE and TEMPERATURE will be essential to answering questions we have around heritability. Another factor that will be included is Dry_mass - which it should be pointed out in this experiment refers to the mass of fish after they were blotted dry with paper towel rather than completely dried out. Larger fish consume more oxygen, therefore, we need to account for this known relationship within our model. Out model will look something like this:

Resting ~ Resting_MALE*Temprature + scale(Dry_mass)

If we had alternative hypotheses to test would would do so at this stage. But in this instance the experiment was designed to answer a specific question via limiting potential covariates.

model1.1 <- glmmTMB(Resting ~ Resting_MALE*Temperature+scale(Dry_mass) + (1|Clutch), 
                    family="gaussian", 
                    data=df)

Great now lets check how out model performed via model validation techniques

Model validation

To check out model performance we will be using two different packages that perform model diagnositics. The packages used here are just examples, there are other packages out there that can provide the same function.

DHARMa

model1.1 |> 
  simulateResiduals(plot=TRUE) 

## Object of Class DHARMa with simulated residuals based on 250 simulations with refit = FALSE . See ?DHARMa::simulateResiduals for help. 
##  
## Scaled residual values: 0.164 0.292 0.04 0.024 0.424 0.496 0.132 0.376 0.42 0.308 0.244 0.144 0.284 0.072 0.116 0.132 0.392 0.956 0.272 0.052 ...
model1.1 |> 
  testResiduals(plot=TRUE)

## $uniformity
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  simulationOutput$scaledResiduals
## D = 0.046101, p-value = 0.5959
## alternative hypothesis: two-sided
## 
## 
## $dispersion
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.0029, p-value = 0.944
## alternative hypothesis: two.sided
## 
## 
## $outliers
## 
##  DHARMa outlier test based on exact binomial test with approximate
##  expectations
## 
## data:  simulationOutput
## outliers at both margin(s) = 3, observations = 278, p-value = 0.4897
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
##  0.002230992 0.031211303
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 ) 
##                                             0.01079137
## $uniformity
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  simulationOutput$scaledResiduals
## D = 0.046101, p-value = 0.5959
## alternative hypothesis: two-sided
## 
## 
## $dispersion
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.0029, p-value = 0.944
## alternative hypothesis: two.sided
## 
## 
## $outliers
## 
##  DHARMa outlier test based on exact binomial test with approximate
##  expectations
## 
## data:  simulationOutput
## outliers at both margin(s) = 3, observations = 278, p-value = 0.4897
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
##  0.002230992 0.031211303
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 ) 
##                                             0.01079137

performance

model1.1 |> check_model(detrend=FALSE)
## `check_outliers()` does not yet support models of class `glmmTMB`.

Partial effect plots

model1.1 |> ggemmeans(~Resting_MALE|Temperature) |> 
  plot(add.data =FALSE)

Model investigations

summary

model1.1 |> summary()
##  Family: gaussian  ( identity )
## Formula:          
## Resting ~ Resting_MALE * Temperature + scale(Dry_mass) + (1 |      Clutch)
## Data: df
## 
##      AIC      BIC   logLik deviance df.resid 
##   -856.7   -824.1    437.4   -874.7      269 
## 
## Random effects:
## 
## Conditional model:
##  Groups   Name        Variance  Std.Dev.
##  Clutch   (Intercept) 0.0004392 0.02096 
##  Residual             0.0022212 0.04713 
## Number of obs: 278, groups:  Clutch, 42
## 
## Dispersion estimate for gaussian family (sigma^2): 0.00222 
## 
## Conditional model:
##                               Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                   0.189873   0.025074   7.573 3.66e-14 ***
## Resting_MALE                  0.003234   0.003800   0.851   0.3947    
## Temperature28.5               0.005710   0.045607   0.125   0.9004    
## Temperature30                 0.085904   0.050048   1.716   0.0861 .  
## scale(Dry_mass)               0.048009   0.003337  14.389  < 2e-16 ***
## Resting_MALE:Temperature28.5  0.002259   0.007202   0.314   0.7538    
## Resting_MALE:Temperature30   -0.008442   0.007386  -1.143   0.2530    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

ANOVA

model1.1 |> Anova()

confint

model1.1 |> confint()
##                                     2.5 %     97.5 %     Estimate
## (Intercept)                   0.140729734 0.23901680  0.189873265
## Resting_MALE                 -0.004213063 0.01068137  0.003234153
## Temperature28.5              -0.083677409 0.09509772  0.005710154
## Temperature30                -0.012188071 0.18399674  0.085904336
## scale(Dry_mass)               0.041469218 0.05454820  0.048008710
## Resting_MALE:Temperature28.5 -0.011857204 0.01637589  0.002259342
## Resting_MALE:Temperature30   -0.022919384 0.00603441 -0.008442487
## Std.Dev.(Intercept)|Clutch    0.014130331 0.03108372  0.020957653

r-squared

model1.1 |> r2_nakagawa()
## # R2 for Mixed Models
## 
##   Conditional R2: 0.566
##      Marginal R2: 0.481

Pairwise comparisons

emmeans [Temperature]

model1.1 |> emmeans(pairwise ~ Temperature, type="response") |> 
  summary(by=NULL, adjust="sidak", infer=TRUE)
## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
##  Temperature emmean      SE  df lower.CL upper.CL t.ratio p.value
##  27           0.213 0.00619 269    0.199    0.228  34.495  <.0001
##  28.5         0.234 0.00851 269    0.213    0.254  27.432  <.0001
##  30           0.246 0.00915 269    0.224    0.268  26.872  <.0001
## 
## Confidence level used: 0.95 
## Conf-level adjustment: sidak method for 3 estimates 
## P value adjustment: sidak method for 3 tests 
## 
## $contrasts
##  contrast                        estimate     SE  df lower.CL upper.CL t.ratio
##  Temperature27 - Temperature28.5  -0.0201 0.0105 269  -0.0453  0.00520  -1.908
##  Temperature27 - Temperature30    -0.0323 0.0111 269  -0.0588 -0.00571  -2.919
##  Temperature28.5 - Temperature30  -0.0122 0.0126 269  -0.0425  0.01801  -0.971
##  p.value
##   0.1626
##   0.0114
##   0.7024
## 
## Confidence level used: 0.95 
## Conf-level adjustment: sidak method for 3 estimates 
## P value adjustment: sidak method for 3 tests

Summary figure

om.rest <- emmeans(model1.1, ~Resting_MALE*Temperature, 
                   at =list(Resting_MALE =seq(from=4, to =10, by=.1)))

om.rest.df <- as.data.frame(om.rest)

om.rest.obs <- drop_na(df, Resting_MALE, Resting) |> 
  mutate(Pred =predict(model1.1, re.form =NA, type='response'), 
         Resid =residuals(model1.1, type ="response"), 
         Fit =Pred + Resid) 

om.rest.obs.summarize <- om.rest.obs |> 
  group_by(Clutch, Temperature) |> 
  summarise(mean.rest =mean(Resting, na.rm=TRUE),
            mean.rest_male =mean(Resting_MALE, na.rm=TRUE),
            sd.rest =sd(Resting, na.rm =TRUE), 
            n.rest = n()) |> 
  mutate(se.rest = sd.rest / sqrt(n.rest), 
         lower.ci.rest =mean.rest - qt(1 - (0.05/2), n.rest -1) * se.rest, 
         upper.ci.rest =mean.rest + qt(1 - (0.05/2), n.rest - 1) * se.rest)|>
  ungroup()
## `summarise()` has grouped output by 'Clutch'. You can override using the
## `.groups` argument.
ggplot(data =om.rest.df, aes(y=emmean, x=Resting_MALE)) + 
  stat_smooth(aes(color=Temperature), 
              method = "lm") + 
  geom_pointrange(data = om.rest.obs.summarize, aes(y =mean.rest, x=mean.rest_male, 
                                                    ymin =lower.ci.rest, 
                                                    ymax =upper.ci.rest, color = Temperature), 
                  alpha =0.2) + 
  facet_wrap(~Temperature) +
  theme_classic() + 
  theme(legend.position ="bottom")
## `geom_smooth()` using formula = 'y ~ x'

Offspring-female

Fit model [fixed factors]

fmodel1.1 <- glmmTMB(Resting ~ Resting_FEMALE*Temperature+scale(Dry_mass) + (1|Clutch), 
                    family="gaussian", 
                    data=df)

Great now lets check how out model performed via model validation techniques

Model validation

To check out model performance we will be using two different packages that perform model diagnositics. The packages used here are just examples, there are other packages out there that can provide the same function.

DHARMa

fmodel1.1 |> 
  simulateResiduals(plot=TRUE) 

## Object of Class DHARMa with simulated residuals based on 250 simulations with refit = FALSE . See ?DHARMa::simulateResiduals for help. 
##  
## Scaled residual values: 0.408 0.484 0.264 0.236 0.156 0.264 0.056 0.132 0.084 0.476 0.964 0.288 0.092 0.88 0.224 0.732 0.284 0.224 0.252 0.236 ...
fmodel1.1 |> 
  testResiduals(plot=TRUE)

## $uniformity
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  simulationOutput$scaledResiduals
## D = 0.063704, p-value = 0.2232
## alternative hypothesis: two-sided
## 
## 
## $dispersion
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.0001, p-value = 0.928
## alternative hypothesis: two.sided
## 
## 
## $outliers
## 
##  DHARMa outlier test based on exact binomial test with approximate
##  expectations
## 
## data:  simulationOutput
## outliers at both margin(s) = 3, observations = 270, p-value = 0.4797
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
##  0.002297266 0.032126194
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 ) 
##                                             0.01111111
## $uniformity
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  simulationOutput$scaledResiduals
## D = 0.063704, p-value = 0.2232
## alternative hypothesis: two-sided
## 
## 
## $dispersion
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.0001, p-value = 0.928
## alternative hypothesis: two.sided
## 
## 
## $outliers
## 
##  DHARMa outlier test based on exact binomial test with approximate
##  expectations
## 
## data:  simulationOutput
## outliers at both margin(s) = 3, observations = 270, p-value = 0.4797
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
##  0.002297266 0.032126194
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 ) 
##                                             0.01111111

performance

fmodel1.1 |> check_model(detrend=FALSE)
## `check_outliers()` does not yet support models of class `glmmTMB`.

Partial effect plots

fmodel1.1 |> ggemmeans(~Resting_FEMALE|Temperature) |> 
  plot(add.data =FALSE)

Model investigations

summary

fmodel1.1 |> summary()
##  Family: gaussian  ( identity )
## Formula:          
## Resting ~ Resting_FEMALE * Temperature + scale(Dry_mass) + (1 |      Clutch)
## Data: df
## 
##      AIC      BIC   logLik deviance df.resid 
##   -829.3   -796.9    423.6   -847.3      261 
## 
## Random effects:
## 
## Conditional model:
##  Groups   Name        Variance  Std.Dev.
##  Clutch   (Intercept) 0.0003942 0.01985 
##  Residual             0.0022631 0.04757 
## Number of obs: 270, groups:  Clutch, 41
## 
## Dispersion estimate for gaussian family (sigma^2): 0.00226 
## 
## Conditional model:
##                                 Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                     0.199816   0.030932   6.460 1.05e-10 ***
## Resting_FEMALE                  0.002294   0.005290   0.434    0.665    
## Temperature28.5                -0.034122   0.065759  -0.519    0.604    
## Temperature30                  -0.009355   0.055819  -0.168    0.867    
## scale(Dry_mass)                 0.049633   0.003453  14.372  < 2e-16 ***
## Resting_FEMALE:Temperature28.5  0.006726   0.009713   0.693    0.489    
## Resting_FEMALE:Temperature30    0.003702   0.007863   0.471    0.638    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

ANOVA

fmodel1.1 |> Anova()

confint

fmodel1.1 |> confint()
##                                       2.5 %     97.5 %     Estimate
## (Intercept)                     0.139191277 0.26044089  0.199816085
## Resting_FEMALE                 -0.008074907 0.01266293  0.002294012
## Temperature28.5                -0.163007674 0.09476402 -0.034121827
## Temperature30                  -0.118757206 0.10004756 -0.009354823
## scale(Dry_mass)                 0.042863948 0.05640139  0.049632667
## Resting_FEMALE:Temperature28.5 -0.012310451 0.02576279  0.006726171
## Resting_FEMALE:Temperature30   -0.011708626 0.01911294  0.003702157
## Std.Dev.(Intercept)|Clutch      0.012980602 0.03036514  0.019853406

r-squared

fmodel1.1 |> r2_nakagawa()
## # R2 for Mixed Models
## 
##   Conditional R2: 0.572
##      Marginal R2: 0.497

Summary figure

om.rest <- emmeans(fmodel1.1, ~Resting_FEMALE*Temperature, 
                   at =list(Resting_FEMALE =seq(from=4, to =10, by=.1)))

om.rest.df <- as.data.frame(om.rest)

om.rest.obs <- drop_na(df, Resting_FEMALE, Resting) |> 
  mutate(Pred =predict(fmodel1.1, re.form =NA, type='response'), 
         Resid =residuals(fmodel1.1, type ="response"), 
         Fit =Pred + Resid) 

om.rest.obs.summarize <- om.rest.obs |> 
  group_by(Clutch, Temperature) |> 
  summarise(mean.rest =mean(Resting, na.rm=TRUE),
            mean.rest_female =mean(Resting_FEMALE, na.rm=TRUE),
            sd.rest =sd(Resting, na.rm =TRUE), 
            n.rest = n()) |> 
  mutate(se.rest = sd.rest / sqrt(n.rest), 
         lower.ci.rest =mean.rest - qt(1 - (0.05/2), n.rest -1) * se.rest, 
         upper.ci.rest =mean.rest + qt(1 - (0.05/2), n.rest - 1) * se.rest)|>
  ungroup()
## `summarise()` has grouped output by 'Clutch'. You can override using the
## `.groups` argument.
ggplot(data =om.rest.df, aes(y=emmean, x=Resting_FEMALE)) + 
  stat_smooth(aes(color=Temperature), 
              method = "lm") + 
  geom_pointrange(data = om.rest.obs.summarize, aes(y =mean.rest, x=mean.rest_female, 
                                                    ymin =lower.ci.rest, 
                                                    ymax =upper.ci.rest, color = Temperature), 
                  alpha =0.2) + 
  facet_wrap(~Temperature) +
  theme_classic() + 
  theme(legend.position ="bottom")
## `geom_smooth()` using formula = 'y ~ x'

Offspring-midpoint

Fit model [fixed factors]

mid_model1.1 <- glmmTMB(Resting ~ Resting_MID*Temperature+scale(Dry_mass) + (1|Clutch), 
                    family="gaussian", 
                    data=df)

Great now lets check how out model performed via model validation techniques

Model validation

To check out model performance we will be using two different packages that perform model diagnositics. The packages used here are just examples, there are other packages out there that can provide the same function.

DHARMa

mid_model1.1 |> 
  simulateResiduals(plot=TRUE) 

## Object of Class DHARMa with simulated residuals based on 250 simulations with refit = FALSE . See ?DHARMa::simulateResiduals for help. 
##  
## Scaled residual values: 0.34 0.424 0.292 0.196 0.14 0.26 0.076 0.112 0.14 0.376 0.952 0.28 0.076 0.804 0.192 0.588 0.228 0.2 0.284 0.216 ...
mid_model1.1 |> 
  testResiduals(plot=TRUE)

## $uniformity
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  simulationOutput$scaledResiduals
## D = 0.053223, p-value = 0.4994
## alternative hypothesis: two-sided
## 
## 
## $dispersion
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.0059, p-value = 0.936
## alternative hypothesis: two.sided
## 
## 
## $outliers
## 
##  DHARMa outlier test based on exact binomial test with approximate
##  expectations
## 
## data:  simulationOutput
## outliers at both margin(s) = 4, observations = 242, p-value = 0.1294
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
##  0.004521472 0.041777518
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 ) 
##                                             0.01652893
## $uniformity
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  simulationOutput$scaledResiduals
## D = 0.053223, p-value = 0.4994
## alternative hypothesis: two-sided
## 
## 
## $dispersion
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.0059, p-value = 0.936
## alternative hypothesis: two.sided
## 
## 
## $outliers
## 
##  DHARMa outlier test based on exact binomial test with approximate
##  expectations
## 
## data:  simulationOutput
## outliers at both margin(s) = 4, observations = 242, p-value = 0.1294
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
##  0.004521472 0.041777518
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 ) 
##                                             0.01652893

performance

mid_model1.1 |> check_model(detrend=FALSE)
## `check_outliers()` does not yet support models of class `glmmTMB`.

Partial effect plots

mid_model1.1 |> ggemmeans(~Resting_MID|Temperature) |> 
  plot(add.data =FALSE)

Model investigations

summary

mid_model1.1 |> summary()
##  Family: gaussian  ( identity )
## Formula:          Resting ~ Resting_MID * Temperature + scale(Dry_mass) + (1 |  
##     Clutch)
## Data: df
## 
##      AIC      BIC   logLik deviance df.resid 
##   -734.6   -703.2    376.3   -752.6      233 
## 
## Random effects:
## 
## Conditional model:
##  Groups   Name        Variance  Std.Dev.
##  Clutch   (Intercept) 0.0004201 0.02050 
##  Residual             0.0023198 0.04816 
## Number of obs: 242, groups:  Clutch, 37
## 
## Dispersion estimate for gaussian family (sigma^2): 0.00232 
## 
## Conditional model:
##                               Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                  0.1925660  0.0299525   6.429 1.28e-10 ***
## Resting_MID                  0.0033761  0.0048251   0.700    0.484    
## Temperature28.5             -0.0430306  0.0711832  -0.605    0.546    
## Temperature30                0.0209171  0.0769909   0.272    0.786    
## scale(Dry_mass)              0.0488705  0.0037304  13.100  < 2e-16 ***
## Resting_MID:Temperature28.5  0.0089635  0.0109691   0.817    0.414    
## Resting_MID:Temperature30    0.0004924  0.0109707   0.045    0.964    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

ANOVA

mid_model1.1 |> Anova()

confint

mid_model1.1 |> confint()
##                                    2.5 %     97.5 %      Estimate
## (Intercept)                  0.133860206 0.25127185  0.1925660287
## Resting_MID                 -0.006080937 0.01283311  0.0033760851
## Temperature28.5             -0.182547042 0.09648582 -0.0430306132
## Temperature30               -0.129982258 0.17181656  0.0209171490
## scale(Dry_mass)              0.041558977 0.05618203  0.0488705046
## Resting_MID:Temperature28.5 -0.012535456 0.03046243  0.0089634891
## Resting_MID:Temperature30   -0.021009706 0.02199453  0.0004924099
## Std.Dev.(Intercept)|Clutch   0.013160323 0.03191940  0.0204955981

r-squared

mid_model1.1 |> r2_nakagawa()
## # R2 for Mixed Models
## 
##   Conditional R2: 0.563
##      Marginal R2: 0.484

Summary figure

om.rest <- emmeans(mid_model1.1, ~Resting_MID*Temperature, 
                   at =list(Resting_MID =seq(from=4, to =10, by=.1)))

om.rest.df <- as.data.frame(om.rest)

om.rest.obs <- drop_na(df, Resting_MID, Resting) |> 
  mutate(Pred =predict(mid_model1.1, re.form =NA, type='response'), 
         Resid =residuals(mid_model1.1, type ="response"), 
         Fit =Pred + Resid) 

om.rest.obs.summarize <- om.rest.obs |> 
  group_by(Clutch, Temperature) |> 
  summarise(mean.rest =mean(Resting, na.rm=TRUE),
            mean.rest_female =mean(Resting_MID, na.rm=TRUE),
            sd.rest =sd(Resting, na.rm =TRUE), 
            n.rest = n()) |> 
  mutate(se.rest = sd.rest / sqrt(n.rest), 
         lower.ci.rest =mean.rest - qt(1 - (0.05/2), n.rest -1) * se.rest, 
         upper.ci.rest =mean.rest + qt(1 - (0.05/2), n.rest - 1) * se.rest)|>
  ungroup()
## `summarise()` has grouped output by 'Clutch'. You can override using the
## `.groups` argument.
ggplot(data =om.rest.df, aes(y=emmean, x=Resting_MID)) + 
  stat_smooth(aes(color=Temperature), 
              method = "lm") + 
  geom_pointrange(data = om.rest.obs.summarize, aes(y =mean.rest, x=mean.rest_female, 
                                                    ymin =lower.ci.rest, 
                                                    ymax =upper.ci.rest, color = Temperature), 
                  alpha =0.2) + 
  facet_wrap(~Temperature) +
  theme_classic() + 
  theme(legend.position ="bottom")
## `geom_smooth()` using formula = 'y ~ x'